This always happens after I've build a few redstone devices. Especially Item Sorters that use a lot of hoppers. This is also accompanied by really REALLY bad low FPS. Riding a minecart is bad too, as it seems to stop and go, stop and go, stop and, well you get the idea.
I've started brand new worlds and everything runs smooth up until I've used about a dozen hoppers and then everything turns to crap with the bad FPS starting all over again.
Facing a certain direction where water is flowing kills the FPS also.
Drinking Potions takes double the time to drink (animation and sound way out of sync too), and the same goes for eating.
TNT taking a very long time to explode.
Clicking buttons to turn on a dispenser take about 4-5 seconds before the actual dispenser turns on.
I've tried Mumbo's trick by covering all uncovered hoppers with half slabs, but that didn't really help.
Saving the game takes a very long time too. I have to move to an area that's far away from my base to save because it's faster saving when I do.
I've tried attached my current world save if you'd like to experience what I'm referring to but site only allows 10MB files to be uploaded and the files are almost 17MB.
I'm on the PS3 single player, online mode and offline, creative and survival. not sure if same thing for xbox